Mini fridge exploits brownian motion

Nano paddle could, in principle, cool a pool of molecules.

Mark Peplow

Just the thing to keep your nano beers cold: an idea for the smallest refrigerator in the world.

The proposal comes from a pair of theoretical physicists, who admit that it would take some spectacularly cunning molecular engineering to make their device a reality. But for now, Chris Van den Broeck from Hasselt University in Belgium and Ryoichi Kawai of the University of Alabama at Birmingham, say the odd trick in their idea will set thermodynamics researchers thinking.

Their proposed device relies on the random jittering of molecules known as brownian motion, named after the botanist Robert Brown, who, in 1827 spotted that bits of pollen under a microscope would not stop jigging around.

In general, the faster the molecules move, the higher their temperature. The proposed miniature refrigerator uses a tiny paddle wheel to speed up the molecules in one pool, thereby sucking the energy out of a neighbouring one.

The idea comes close to an amusing thought experiment proposed by the physicist James Clerk Maxwell in the nineteenth century: Maxwell said an imaginary demon might be able to make one pot of molecules hotter and another colder by strategically opening and closing a portal between the two, allowing only the faster, hotter molecules through.

But Van den Broeck and Kawai propose something slightly more achievable than using a demon.

Spin me round

Their idea essentially reverses a previous notion physicists have had about how to use two pools with different temperatures to make a mini motor.

Spin me round: the top paddle faces more resistance from surrounding molecules when spun counter-clockwise.

Imagine a vertical shaft that connects a bottom wheel with flat paddles, and a top one with wedge-shaped paddles (see picture); the two paddles are sitting in different pools of molecules that are separated by an insulating barrier.

If the bottom pool were very hot, with molecules whizzing around, and the top one sedately cool, then the bottom paddle would get whacked quite often by particles, sending it spinning in either direction.

When the wheel is sent spinning counter-clockwise, the top paddle thwacks into surrounding molecules with its blunt edge, which slows the wheel down. But when it spins clockwise, the top paddle slices through the molecular soup with its sharp edge providing less resistance. So, after lots of collisions striking the bottom paddle, the wheel would be expected to make a net movement clockwise.

Upside down

Van den Broeck and Kawai have simply turned this idea on its head.

In their model, the two pools start out at the same temperature. Then a motor is used to drive the bottom paddle wheel around counter-clockwise. One principle of thermodynamics says that the system will respond by trying to induce a counteractive force in a clockwise direction. As just described, this can happen if the bottom pool gets much hotter than the top one.

The intriguing thing is that the researchers calculate, using standard equations of thermodynamics, that this can not only heat up the bottom pool, but actually cool the top one down.

Cool stuff

Although this result falls out of the maths, it isn't clear exactly how the molecules behave in a way that actually slows down their motion in the top pool. "If it were easy to understand, people would have found this much earlier," says Van den Broeck. "You can't explain it by hand waving; it's a statistical thing." The concept, now available on arXiv1, is scheduled for publication in Physical Review Letters.

"It's not a big effect — actually, it's minute," notes Anders Kastberg, a physicist at Umeå University, Sweden. "But you have to start somewhere. It's a cute idea and a new mechanism as far as I know."

ADVERTISEMENT

It may be some time before your nano beers reach optimum temperature, however. Making a device to drive a mini wheel around would be particularly tricky. Van den Broeck suggests that lasers or magnets might be used, but he admits that's on the borderline of what is feasible. "I like theoreticians," laughs Kastberg. "They don't have to bother about reality."

Just the thing to keep your nano-beers cold: an idea for the smallest refrigerator in the world.